The Goldbach Conjecture dates back to 1742 when a German mathematician called Christian Goldbach wrote a letter to Leonhard Euler containing observations about prime numbers. One such consideration is “Every integer greater than two can be written as the sum of three primes.” Euler became fascinated with the problem and answered the version of the conjecture that “Every even integer greater than 2 is the sum of two prime numbers” he confirmed that he regarded the theorem to be true (“Ein Ganz Gewisses Theorema”). Still, he was not able to prove it.
A prime number is any number divisible by one and itself, therefore let us try and test the Goldbach Conjecture: It states for every integer N, and N>2, then N= P1+P2. In this case, then P1 and P2 have to be prime numbers.
4=2+2 where 2 is a prime number, and as such, the answer is “yes” for the number 4.
6=4+2 where both 4 and 2 are prime numbers, thus we confirm it is valid for the number 6.
8=6+2 where 6 and 2 are both prime numbers, so that is another affirmative prove to the theory.
All prime numbers that are greater than 2 are odd, and since the sum of two odd numbers is always even then Goldbach conjecture is true.
In 1938 another mathematician Nils Piping confirmed the Goldbach conjecture to hold for numbers up to and including 100,000. It was again tested using a computer search up to 4×10^18 and held. According to Stewart (2014), as the numbers in question get bigger, there tend to be multiple ways the number can be written as a sum of primes.